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Systematic challenges in future dark energy measurements John Peacock Tokyo HSC Workshop Nov 2006 ESA-ESO Working Group on Fundamental Cosmology John Peacock (Chair) Peter Schneider (Co-Chair) George Efstathiou Jonathan R. Ellis Bruno Leibundgut Simon Lilly Yannick Mellier Major contributors: Pierre Astier, Anthony Banday, Hans Boehringer, Anne Ealet, Martin Haehnelt, Guenther Hasinger, Paolo Molaro, Jean- Loup Puget, Bernard Schutz, Uros Seljak, Jean-Philippe Uzan Dark Energy Task Force Report to NSF, DoE, NASA Rocky Kolb Andy Albrecht Cosmology: Concordance Model Heavy elements 0.03% Neutrinos 0.3% Stars 0.5% H + He gas 4% Dark matter 20% Dark Energy 75% Outstanding questions: • initial conditions (inflation?) • nature of the dark matter • nature of the dark energy The cosmological parameters Only 6 parameters needed (flat; no gravity waves) Normalization Optical depth from reionization Scalar spectral index WMAP3 + 2dFGRS Baryon density ( = h2) CDM density ( = h2) H0 / 100 + r (tensor fraction), curvature, m , w ´ P/ (DE eqn of state) DE is entangled with other parameters The nature of dark energy (1) Zero-point energy? ) expect vac » Emax4 (natural units: c=h=1) But empirically Emax = 2.4 meV - not a real cutoff (2) Dynamical ‘Dark Energy’ - ‘Quintessence’: use inflationary technology of w<0 from scalar fields - Empirical w= P/ c2 (= -1?); fit w(a) = w0 + wa(1-a) Dark Energy: sensitivity distance & degeneracy Vacuum affects H(z): H2(z) = H20 [ M (1+z) 3 + R (1+z) 4 + V (1+z) 3 (1+w) ] matter radiation vacuum Alters D(z) via r = s c dz / H And growth via 2H d/dt term in growth equation Rule of 5 Both effects are (1) Small (need D to 0.2% for w to § 1%) (2) Degenerate with changes in m growth To measure w to a few %, we need to have independent data on m and to be able to control systematics to a few parts in 1000 − even harder with lensing (rule of 10) Dark energy: current status Combined: Need to aim for 1% precision in future work Ruling in L: Bayesian view Evidence ratio: trade likelihood ratio against how much of parameter space is ruled out Trotta (2005): roughly 1% accuracy on w will prove it’s L unless we measure a large likelihood against that model Evolving Dark Energy: pivot redshifts Assume w = w0 + wa(1-a) If observe degeneracy w0 = A + Bwa, ) w = A + (B+1-a)wa ) zpivot = 1/(1+B) - 1 Method zpivot CMB 0.43 BAO z=1 0.54 Difficult to get much baseline BAO z=1+z=3 0.85 Lensing 0.25 Not everything may fit: new physics, or systematics? − need for multiple independent methods − harder in future The CMB: common basis for all methods CMB degeneracies and w Comoving distance-redshift relation: ( = h2) CMB power spectrum depends only on m and b (apart from large-scale ISW and reionization) Thus degeneracy between curvature and vacuum (vary both to keep D fixed) Flat case: vary v and w. Degeneracy broken by large-scale effects. Thus limit on w from good CMB data alone Lensing vs SNe vs BAO (Dune) (SNAP) (WFMOS 5000) And similar constraints from mass function of 100,000 clusters DETF likes w0 £ wa but not so clear – kill L first Probe 1: Supernovae Ground vs HST Standard candles: distances to 5% Currently samples of few hundred Space resolution essential for high z Supernovae: Future challenges Now: ~500 SNe (SNLS). 2010: ~5,000 (Pan-STARRS) Could yield w to 2%, but: – Photometric accuracy to < 1% needed – Malmquist worries at higher z – Contamination by non-Ia – Non-MW extinction – Evolution of these factors, even ignoring intrinsic evolution Probe 2: Gravitational lensing Image distortion depends on − D(z) via baseline − growth of structure Shear Data: Ground vs Space Typical cosmic space shear is ~ 1%, and must be measured weak lensing shear with high accuracy Even so, 1% precision on w ground needs > 10,000 deg2 surveys Space: small and stable PSF larger number of resolved galaxies reduced systematics Photometric redshifts Broad-band data can give z/(1+z) ' 0.04 But expect catastrophic failures for z>1 with optical only Sufficiently deep near-IR (K ' 22) needs space Lensing: future challenges PSF correction: STEP testing shows that even measuring shear with 1% precision is hard. Photo-z precision: need to know <z> in a few tomographic z bands to 0.1% fractional accuracy – needs >105 z’s to calibrate Nonlinear corrections: most observations to date probe only shear correlations < 10 arcmin – need more accurate models for nonlinear P(k) – effect of baryons? Intrinsic effects: – alignment of close pairs – foreground-background alignments Probe 3: Clusters of galaxies Evolving mass function sensitive to g(z) Apparent baryon fraction depends on D(z) Clusters: future challenges Projection effects: Need X-ray survey (eROSITA?) Mass estimates: – Accuracy of mass estimation from X-ray/SZ (8% rms) – Self-calibration to avoid bias in masses Redshift accuracy: – need z/(1+z) ' 0.02 – Maybe OK via averaging photo-z’s – but needs 105 z’s for calibration in any case Probe 4: P(k) and Baryon oscillations (1) Matter-radiation horizon: 123 (m h2 / 0.13)-1 Mpc (2) Acoustic horizon at last scattering : 2 -0.25 2 -0.08 147 (m h / 0.13) (b h / 0.024) Mpc Standard rulers to probe distance-z relation BAO: Precision on D(z) and volume Takada % error in D = (V / 5 h-3 Gpc3)-1/2 £ (kmax / 0.2 h Mpc-1)-1/2 0.7 < z < 1.3: 1 (h-1Gpc)3 = 540 deg2 2.5 < z < 3.5 : 1 (h-1Gpc)3 = 254 deg2 Thus 1% distance accuracy (5% on w) needs 2000 (z=1) or 1000 (z=3) deg2 Really prefer > 5000 deg2 at z = 1 (>5 million z’s) z = 3 selection problematic BAO with Photo-z’s Schuecker Much less efficient: e.g. ESO VST/KIDS, 60 million photo-z over 1500 deg2 gives 14% predicted error on w: ~100 times bigger sample needed for same accuracy as WFMOS Possibly interesting with all-sky data, but demanding on photometric uniformity Systematics Need to show that acoustic scale is at linear prediction to few parts in 1000 Why might it not be?: • Mass nonlinearities • Scale-dependent bias • Mask convolution • Missing close pairs Needs many semi-realistic mock surveys Semianalytic galaxies in MS: 1014M¯ halo Dark matter Galaxies Galaxy power: bigger ‘nonlinear’ effects at z=3 than at z=1 z=7 z=3 DM gals Power spectrum from MS divided by a baryon-free LCDM spectrum z=1 z=0 Springel et al. 2005 Larger volumes: mock galaxy P(k) data Semianalytic data from Durham 1 Gpc/h cube (ICC1000) Systematic shift in oscillation scale relative to linear theory of ~1% Can plausibly calibrate this down to 0.1% shift Pan-STARRS 1 1.8m telescope on Haleakala, Maui 7 deg2 OT CCD camera Survey operations from mid-2007 – Initial programme runs to end 2010 – 20,000 deg2 grizy to i=23.8 – 84 deg2 grizy to i=27.0 Most powerful imaging cosmology data prior to DES, HSC – Should get w to 2-3% from each of lensing, SNe, photo-z BAOs Science consortium: Hawaii, MPG Germany, CfA, JHU, UK (Belfast, Durham, Edinburgh)

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